You can change the start date of a work item from the header of your work item. Click on 'Due' to reveal the option to update the start date and due date of that work item.
Alternatively, you can also edit the start date of a work item from the 'Key Dates' section of the Details tab.
If the work item has any tasks with due dates set, changing the start date will present a modal giving you the opportunity to leave task due dates as they are, or update them the same number of days forward or backward that you are changing the start date.
Keep in mind when you change the start date on a work item, this will not affect any future work that is on the repeating schedule of that work item. To update the start date for future work, see below.
Updating the start date of future work on a schedule
When making changes to work within a schedule, it is important to be aware that not all data will get carried over to future work in the same way.
When making changes to the start date or how often the work repeats for the future, you will need to go into the repeat settings of the work item and select 'Delete Repeat'.
Once you have deleted the repeat schedule on the work item, you will then be able to change the start date and make changes to your entire repeat settings and set up a repeating work schedule again.
Keep in mind when you delete the repeating work, if your first work item is in 'Planned Status' and has not yet reached the start date, that work item will also be deleted.